Lehmer-type bounds and counting rational points of bounded heights on Abelian varieties

IF 0.5 3区数学 Q3 MATHEMATICS International Journal of Number Theory Pub Date : 2024-05-29 DOI:10.1142/s1793042124501045

Narasimha Kumar, Satyabrat Sahoo

引用次数: 0

Abstract

In this paper, we study Lehmer-type bounds for the Néron–Tate height of $\bar{K}$ -points on abelian varieties $A$ over number fields $K$ . Then, we estimate the number of $K$ -rational points on $A$ with Néron–Tate height $\leq log B$ for $B ≫ 0$ . This estimate involves a constant $C$ , which is not explicit. However, for elliptic curves and the product of elliptic curves over $K$ , we make the constant explicitly computable.

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阿贝尔变体上的雷默型边界和有界高的有理点计数

在本文中，我们研究了数域 K 上的无性变项 A 上 K̄ 点的奈伦-塔特高度的雷默型边界。然后，我们估计了 B≫0 时 A 上奈伦-塔特高度≤logB 的 K 有理点的数量。这个估计涉及一个常数 C，它并不明确。然而，对于椭圆曲线和 K 上的椭圆曲线乘积，我们可以明确地计算这个常数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.

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